The typical image of a chief executive is a smartly-dressed man or woman in a boardroom or behind a desk.

Not so John Legere, the U.S. CEO and president of telecommunications company T-Mobile, who spends his day dressed in a company-branded tracksuit top and pink t-shirt and is often on social media.

The first thing he does each day is check Twitter, writing tweets to his 4.7 million followers. "I probably do 6 to 7 hours a day just on social," he told CNBC's "The Brave Ones."

CEOs need to write their own tweets or risk being seen as phony, he added. "You know one of the things you can't do in social is, it has to be you, if it ever becomes — and they can tell — if it's somebody being you, they vote you off the island."

One of his famous followers is rapper Snoop Dogg, who featured in T-Mobile's Super Bowl commercial this year with Martha Stewart.

Stewart and Snoop have their own cookery show, "Martha & Snoop's Potluck Dinner Party," currently airing on VH1, and in January posted a tweet asking Legere to appear on it.

Legere also told "The Brave Ones" he likes to use social media to show off to his family.

"My daughters, they'll want to talk to so and so (celebrity) and I'll say: 'Watch this' and I'll text (trance group) Above and Beyond or I'll text Snoop Dogg and she'll say: 'You kidding me? Why would Snoop text you?' And I'll say: 'Honey, they all follow me on Twitter'," he said.

T-Mobile's U.S. operation is currently in talks to merge with Sprint, but discussions were said to be stalling Monday.